The point with coordinates $(6,-10)$ is the midpoint of the segment with one endpoint at $(8,0)$. Find the sum of the coordinates of the other endpoint.
Let the other endpoint be $(x,y)$. We have the equations $(x+8)/2=6$ and $(y+0)/2=-10$, or $x=4$ and $y=-20$. The sum of the coordinates is $4+(-20)=\boxed{-16}$.