Answer
$\{-63,28\}$
Work Step by Step
Step 1. Let $u=(x-1)^{1/3}$, we have $u^2+u-12=0$
Step 2. Factor and solve: $(u+4)(u-3)=0$ thus $u=-4, 3$
Step 3. For $u=-4$, we have $(x-1)^{1/3}=-4$ or $x-1=-64$ and $x=-63$
Step 4. For $u=3$, we have $(x-1)^{1/3}=3$ or $x-1=27$ and $x=28$
Step 5. Solution set $\{-63,28\}$