Answer
$\{\frac{1}{4}, 1\}$
Work Step by Step
Step 1. Given the equation as $(2x-1)^{2/3}=(x)^{1/3}$
Step 2. Raise both sides to the 3rd power to get: $(2x-1)^2=x$ or $4x^2-5x+1=0$ which gives $x=\frac{1}{4}, 1$
Step 3. Check answers in the original equation: $\{\frac{1}{4}, 1\}$ fit.