This question gets asked quite often.
The short answer is that you can do long distance rides on basically any bicycle as long as it’s comfortable for you.
There are a few things you can do to your bicycle to make it more efficient and easier:
Make sure your seating position is good.
Especially that your saddle is high enough.
This will improve power output and reduce risk of knee pain/injuries.
Reduce air resistance by lowering the handlebar.
If you have front suspension, lock it (or get a rigid fork).
Wear tight fitting bicycle clothes.
Keep it well maintained.
Get road bike tires with low rolling resistance.
Get clipless pedals and shoes.
In the end the most important part will still be training.
Training for long distance rides basically boils down to riding a lot.
During long rides nutrition (and of course hydration) is also very important.
bicycles.stackexchange.com/users/19529/Michael
You can certainly do Brevet Populaires (100 km).
Plenty of people do them on all sorts of bikes.
I've seen a few people on flat bars on Brevets de Randonneurs 200 in the UK, including an MTB with knobbly tyres ( the one with the backpack in this picture ).
Hybrids on these rides tend to be set up as flat bar road bikes, i.e. smoothish tyres around 25-35 mm and to have gearing comparable to a tourer.
I don't think I've seen flat bars on a 300 (but I'm doing one tomorrow
so I'll try to remember to look out for them).
You might end up as a full-value rider (i.e. close to the time limit) especially if there's a headwind, but no-one will think any the worse of you for your choice of bike.
One day I may do a 100 on my hybrid but not with its current saddle - hybrid saddles can be rather fat and chafe.
bicycles.stackexchange.com/users/7309/Chris H
In practice, most people find hybrids rather uncomfortable for long rides.
What "long" means varies from person to person so, to a large extent, you'll just have to try going on longer and longer rides until you find out what your body is comfortable with.
I would note, though, that 40 minutes at the 11mph you said you average in your other question is a long way from brevet-style riding.
Don't try to run before you can walk.
bicycles.stackexchange.com/users/13174/David Richerby
Two summers ago I rode 1,300 miles around Lake Superior on a Trek Verve 2, averaging about 70 miles a day.
I am over 60 years old, and I like a more comfortable ride at this stage.
The more durable tire of a hybrid came in handy when I needed to navigate rougher terrain.
These days I am riding a Specialized Cross Trail on long rides.
I love it.
bicycles.stackexchange.com/users/43472/Lawrence Ely
Last year I rode the Houston MS-150 on a hybrid.
This year some guy rode it on a penny-farthing.
Your bike should be no problem, as long as it's a bike that fits you.
bicycles.stackexchange.com/users/33422/EvilSnack
My experience is that pretty much any bike can do pretty much any type of ride (within reason; a track bike cannot do mud racing, for example).
I’ve done a 160 km ride (60 km sportive, 20 km to get there and 80 km to get home) on a fixed gear bike with narrow raiser bars.
That worked fine.
Was it the ideal bike for such a long ride through mostly countryside?
Certainly not.
But it was still very enjoyable.
An endurance bike would have been faster.
A tourer would have been more comfortable.
But it was fine.
A hybrid would have worked, too.
Heck, even a town bike can do that; it just takes a very long time.
This weekend just passed as of writing this answer, I did maybe 100-120 km around the southeast of Scania in the south of Sweden, on a gravel bike.
It has the same 700x35C tyre size as on your bike.
35 mm tyres are fine even on long stretches of road; the rolling resistance is comparable to the 28 mm tyres on my fixie, but the ride is more comfy.
I find that on longer rides, the different hand positions of drop bars really help.
If possible, I would recommend looking into a different handlebar.
The typical wide, mostly flat bar that most hybrids have gets really uncomfortable after a while.
Look for something that gives you a few different hand positions.
That’s probably the single most important upgrade you can do to your bike for longer rides.
bicycles.stackexchange.com/users/43514/Simon Lundberg
I have a hybrid bike with 27" large frame,  700c wheels and 35mm tires. Can I do brevets (long distance ride) on this bike? If yes, what are the points I should start working on to achieve this? Currently I am a beginner and riding around 40 minutes per day and little more on weekends.
Can I do brevets (long distance rides) on my hybrid bike? If yes, how to start?
bicycles.stackexchange.com
<hybrid-bike><long-distance>
bicycles.stackexchange.com/questions/61855
bicycles.stackexchange.com/users/43401/harsha.cs
S1: The short answer is that you can do long distance rides on basically any bicycle as long as it’s comfortable for you.  You can certainly do Brevet Populaires (100 km). Plenty of people do them on all sorts of bikes.  Your bike should be no problem, as long as it's a bike that fits you. Things you may wish to consider are the position of the seat, lower handlebars, getting tires with low rolling resistance, getting clipless pedals and shoes and wearing tight bicycle clothing. People use different kinds of bikes on these rides, and a well-fitting hybrid will be fine if you have the required fitness level yourself. Make sure that the bike fits you and is well maintained, and wear suitable clothing. A bike can be adapted for longer rides by adjusting the handlebars for lower wind resistance, using smoother tyres, locking the suspension and using clipless pedals. Some people find drop handlebars more comfortable on longer rides, in addition to being more aerodynamic.
People use different kinds of bikes on these rides, and a well-fitting hybrid will be fine if you have the required fitness level yourself. Make sure that the bike fits you and is well maintained, and wear suitable clothing. A bike can be adapted for longer rides by adjusting the handlebars for lower wind resistance, using smoother tyres, locking the suspension and using clipless pedals. Some people find drop handlebars more comfortable on longer rides, in addition to being more aerodynamic.