Answer
$ 1$ and $ 4$.
Work Step by Step
Given $(x-2)^{2/3}=x^{1/3}$, raise both sides to the $3rd$ power to get $((x-2)^{2/3})^3=(x^{1/3})^3$ or $(x-2)^2=x$, thus $x^2-4x+4=x$, $x^2-5x+4=0$ which gives $x=1$ and $x=4$.
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