if $x +2^{1/3}+2^{2/3}=0$ then find the value of $x^3+6$?

Question

if $x +2^{1/3}+2^{2/3}=0$ then find the value of $x^3+6$?

Answer 1

$$x=-2^{1/3}-2^{2/3} \implies x^3=-2-4+3.2(x)=-6+6x \implies x^3+6=6x$$