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 $l+m+n$?

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