Fast way to solve $4 = \sqrt[3] {x+10}-\sqrt[3] {x-10}$ The question is this:
$4 = \sqrt[3] {x+10}-\sqrt[3] {x-10}$
For some reason, I keep on getting 289/3, even though it is the wrong answer. This is from a timed test, and my way is wrong and extremely slow.

Use this formula $$\boxed{(a-b)^3 = a^3-3ab(a-b)-b^3}$$
$$4 = \sqrt[3] {x+10}-\sqrt[3] {x-10}\;\;\;/^3$$
$$64 = x+10 -3\sqrt [3]{(x+10)(x-10)}(\underbrace{\sqrt[3] {x+10}-\sqrt[3] {x-10}}_{4})-x+10$$
So $$11 = -3\sqrt [3]{x^2-100}\implies x = \pm\sqrt{{-11^3\over 27}+100}$$
