Step 1: 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, $\sqrt[3]{216} = 6$. Step 2: Evaluate the cube root of 125. 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, $\sqrt[3]{125} = 5$. Step 3: Add the results from Step 1 and Step 2. $$ \sqrt[3]{216} + \sqrt[3]{125} = 6 + 5 $$ $$ 6 + 5 = 11 $$ The final answer is $\boxed{11}$. Last free one today — make it count tomorrow, or type /upgrade for unlimited.