8. Given $\sqrt[3]{x^{2}}+\sqrt[3]{(35-x)^{2}}=13$. Then $\sqrt[3]{x}+\sqrt[3]{35-x}=$ $\qquad$ .
8. 2,5 .

Let $\sqrt[3]{x}=m, \sqrt[3]{35-x}=n, a=m+n, b=m n$.
Then $m^{2}+n^{2}=13$, i.e.,
$$
a^{2}-2 b=13 \text {; }
$$
$m^{3}+n^{3}=x+(35-x)=35$, i.e.,
$$
a^{3}-3 a b=35 \text {. }
$$

From equations (1) and (2), eliminating $b$ gives
$$
a^{3}-39 a+70=0 \text {. }
$$

Solving yields $a=5,2,-7$ (-7 is discarded).