Answer
$\{\frac{2}{5}, 1\}$
Work Step by Step
Step 1. Rewrite the equation as $\sqrt[3] {5x^2-6x+2}=\sqrt[3] {x}$
Step 2. Raise 3rd power on both sides to get: $5x^2-6x+2=x$ or $5x^2-7x+2=0$ which gives $x=\frac{2}{5}, 1$
Step 3. Check answers in the original equation: both $\{\frac{2}{5}, 1\}$ fit.
