ÖMO 1998 Problem 1

Let $a \geq 0$ be a natural number. Determine all rational $x$ , so that $$\sqrt{1+(a-1)\sqrt[3]x}=\sqrt{1+(a-1)\sqrt x}$$ All occurring square roots, are not negative.Note. It seems the set of natural numbers = $\mathbb N = \{0,1,2,\ldots\}$ in this problem.