<s>[INST] Find the meaning of the expression $\sqrt[3]{19 - a} + \sqrt[3]{10 - a}$, if $\sqrt[3]{19 - a} - \sqrt[3]{10 - a} = 1$. 
Find the meaning of the expression $\sqrt[3]{19 - a} + \sqrt[3]{10 - a}$, if $\sqrt[3]{19 - a} - \sqrt[3]{10 - a} = 1$.

What i tried:
$$\sqrt[3]{19 - a} = m $$
$$\sqrt[3]{10 - a} = n $$
$$ m - n = 1 $$
$$ m = 1 + n $$
$$ (1 + n) + n = 1 + 2n  =$$
$$ ... $$
 [/INST] Also, $$m^3-n^3=\left(\sqrt[3]{19-a}\right)^3-\left(\sqrt[3]{10-a}\right)^3=19-a-(10-a)=9,$$ which gives $$m^2+mn+n^2=9$$ or
$$1+3mn=9$$ or
$$mn=\frac{8}{3},$$ which gives $$m^2+2mn+n^2=9+\frac{8}{3}$$ or
$$(m+n)^2=\frac{35}{3},$$ which gives $$m+n=\sqrt{\frac{35}{3}}$$ or $$m+n=-\sqrt{\frac{35}{3}}.$$
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