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.

[b]Note.[/b] It seems the set of natural numbers = $\mathbb N = \{0,1,2,\ldots\}$ in this problem.