For this question, my first idea was to substitute $a = (x + 1)^{\frac{1}{3}}$ and $b = (x - 1)^{\frac{1}{3}}$. I then get the equation $a^2 + 4b^2 = 5ab$. I completed the square and got $(a - 2b)^2 = ab$. I thought I could construct a quadratic with $a$ and $b$ as the roots, but I do not think I can do that very easily. Are there any other strategies that I could try for this problem? Thank you.