Answer
$-30,5$.
Work Step by Step
Step 1. Let $u=(x+3)^{1/3}$, we can rewrite the original equation as $u^2+u-6=0$
Step 2. Factor the equation to get $(u+3)(u-2)=0$, thus $u=-3$ and $u=2$
Step 3. For $u=(x+3)^{1/3}=-3$, we have $x+3=(-3)^3=-27$, thus $x=-30$
Step 4. For $u=(x+3)^{1/3}=2$, we have $x+3=(2)^3=8$, thus $x=5$
Step 5. Both answers fit the original equation, thus the solutions are $x=-30$ and $x=5$.
