35. Simplifying Radicals. Simplify the expression

$$
\sqrt[3]{2+\sqrt{5}}+\sqrt[3]{2-\sqrt{5}}
$$
35. Let $\sqrt[3]{2+\sqrt{5}}=a, \quad \sqrt[3]{2-\sqrt{5}}=b, \quad a+b=x$. Then

$$
x^{3}=a^{3}+3 a^{2} b+3 a b^{2}+b^{3}=a^{3}+b^{3}+3 a b(a+b)=4+3(\sqrt[3]{-1}) x
$$

Thus, $x^{3}+3 x-4=0$, and the only real root of this equation is 1.

$[$ [K. Adler, A. M. M., 59, 328 (May 1952).]