Titu's upside down

Algebra Level 5

Consider all \(x,y,z\) positve reals that satisfy,

\[ \frac1x + \frac1y+\frac1z=\frac{11}6. \]

If the minimum value of \(x+ \frac y4 +\frac z9 \) is in the form of \(\frac ab\) for coprime positive integers \(a,b\). Find \(a+b\).

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