Simple AM-GM Application

Algebra Level 4

The minimum value of ax3+by3+cz2+dxyzax^3+by^3+cz^2+\frac{d}{xyz} for fixed aa, bb, cc, d>0d > 0 and x,y,z0x, y, z \geq 0 can be written in the form na2b2c3d6nl9/nm10/n\dfrac{n\sqrt[n]{a^2b^2c^3d^6}}{l^{9/n}m^{10/n}}, where ll, mm, and nn are positive integers. What is l+m+nl+m+n?

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