Evaluate the cube root of 216.

We need to find a number that, when multiplied by itself three times, equals 216.

$$6 \times 6 \times 6 = 36 \times 6 = 216$$

So, $\sqrt[3]{216} = 6$.

We need to find a number that, when multiplied by itself three times, equals 125.

$$5 \times 5 \times 5 = 25 \times 5 = 125$$

So, $\sqrt[3]{125} = 5$.

$$\sqrt[3]{216} + \sqrt[3]{125} = 6 + 5$$ $$6 + 5 = 11$$

The final answer is 11.