Solution
= Solution
For real cube roots, set $u=a^{1/3}$ and $v=b^{1/3}$, so $(ab)^{1/3}=uv$. The <sum of two cubes> identity gives
$$
(u+v)(u^2-uv+v^2)=u^3+v^3=\boxed{a+b}.
$$
= Solution
For real cube roots, set $u=a^{1/3}$ and $v=b^{1/3}$, so $(ab)^{1/3}=uv$. The <sum of two cubes> identity gives
$$
(u+v)(u^2-uv+v^2)=u^3+v^3=\boxed{a+b}.
$$