# Perfect commons

Number Theory Level pending

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

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 $$\overline{x_1x_2x_3\ldots x_n}$$.

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