Perfect commons

$\large \begin{cases} a = \sqrt[3]{\overline{Z \cdots X}} \\ b = \sqrt{\overline{Z \cdots X}} \end{cases}$

Given that $X$ is the last digit of a very large number, $\overline{Z \cdots X}$ and $a$ is a positive integer while $b$ is not an integer.

If $x_1,x_2,x_3,\ldots, x_n$ , such that $x_1<x_2<x_3< \ldots<x_n$ , are the possible values of $X$ , submit your answer as $\overline{x_1x_2x_3\ldots x_n}$ .