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 \(l+m+n\)?