Simple AM-GM Application

Algebra Level 4

The minimum value of $ax^3+by^3+cz^2+\frac{d}{xyz}$ for fixed $a$ , $b$ , $c$ , $d > 0$ and $x, y, z \geq 0$ can be written in the form $\dfrac{n\sqrt[n]{a^2b^2c^3d^6}}{l^{9/n}m^{10/n}}$ , where $l$ , $m$ , and $n$ are positive integers. What is $l+m+n$ ?