Answer
$x=125$ or $x=1$
Work Step by Step
We simplify as follows:
$x^{\frac{2}{3}}-6x^{\frac{1}{3}}+5=0$
Let $m=x^{\frac{1}{3}}$
$m^{2}-6m+5=0$
$(m-5)(m-1)=0$
$m-5=0$ or $m-1=0$
$m=5$ or $m=1$
$x^{\frac{1}{3}}=5$ or $x^{\frac{1}{3}}=1$
$x=(5)^{3}$ or $x=(1)^{3}$
$x=125$ or $x=1$
