+212 Simplify $\sqrt[3]{\frac{9\sqrt{5}}{2\sqrt{3}}\cdot\frac{5\sqrt{2}}{8\sqrt{2}}}$ and rationalize the denominator. The result can be expressed in the form $\frac{\sqrt{a}\sqrt[3]{b}}{c}$, where $a$, $b$, and $c$ are positive integers. What is the minimum possible value of the sum $a+b+c$?
