Rationalize the denominator of \(\displaystyle \frac{1}{\sqrt[3]{3} - \sqrt[3]{2}}\). With your answer in the form \(\displaystyle \frac{\sqrt[3]{A} + \sqrt[3]{B} + \sqrt[3]{C}}{D}\) and the fraction in lowest terms, what is \(A + B + C + D\)?
The expression simplifies to \(\dfrac{\sqrt[3]{12} + \sqrt[3]{18} + \sqrt[3]{36}}{2}\)
Therefore, the answer is 12 + 18 + 36 + 2 = 68.
+8 
