Square trouble

Calculus Level 4

If

\[\large{f(x, y, z) = \ln(x^3+y^3+z^3-3xyz)}\]

Then

\(\Large{\left(\frac{\partial}{\partial x}+\frac{\partial}{\partial y}+\frac{\partial}{\partial z}\right)^{2} f = -\frac{A}{(x+y+z)^{B}}}.\)

Find \(A+B.\)


Note: Expanding \(\left(\frac{\partial}{\partial x}+\frac{\partial}{\partial y}+\frac{\partial}{\partial z}\right)^{2}\) means to sum all nine possible second derivatives.

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