$\displaystyle \left ( m^\frac{1}{3}+n^{\frac{1}{3}} \right )\left ( m^{\frac{2}{3}}-m^{\frac{1}{3}}n^{\frac{1}{3}}+n^{\frac{2}{3}} \right )$
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Try either expanding by brute force, or using the sum of two cubes rule.
$\displaystyle ...=\left ( m^{\frac{1}{3}} \right )^{3}+\left ( n^{\frac{1}{3}} \right )^{3}=m+n$
Originally Posted by Lil $\displaystyle ...=\left ( m^{\frac{1}{3}} \right )^{3}+\left ( n^{\frac{1}{3}} \right )^{3}=m+n$ correct
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