Inspired by Lakshya Sinha

Algebra Level 4

Find the minimum value \(m\) and the maximum value \(M\) of \[f(x,y,z)=x^3+\frac{y^3}{4}+\frac{z^3}{9}\] when \(x+y+z=12\), where \(x,y\) and \(z\) are non-negative real numbers. Enter \(m+M\).

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