Can you make it the best?

Let \((x, y, z)\) be any one positive integral solution to
\[\large\ \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{2^n}{3^n}\] where \((a,b,n)\) are positive integers, such that \(x + y +z\) is maximal.

Find the value of \(x + y +z\).

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