Calculate :
$\displaystyle
\sqrt[3]{2+11i}+\sqrt[3]{2-11i}
$
I guess one method would be:
$\displaystyle z^3=2+11i$
$\displaystyle (a+bi)^3=2+11i$
$\displaystyle a^3-3ab^2+(3a^2 b-b^3)i=2+11i$
Then you would have two equations to solve for the first term in the problem: $\displaystyle a^3-3ab^2=2$ and $\displaystyle 3a^2 b-b^3=11$