If x=(a+sqrt(a^2+b^3))^(1/3)+(a-sqrt(a^2+b^3))^(1/3) then prove: x^3+3bx=2a

If $x={(a+\sqrt{a^2+b^3})}^{1/3}+{(a-\sqrt{a^2+b^3})}^{1/3}$ prove that $x^3+3bx=2a$