Base of number base

There is a number \(a\), which can be written as \(\overline{xyz}\) in base 9 and \(\overline{zyx}\) in base 6, for some positive integer \(x,y,z\). Find \(x+y+z\).

Details and Assumption

\( \overline{xyz} \) represents reading the digits together, instead of multiplying them out. For example, \( \overline{xyz}_9 = 81 x + 9y + z \) and \( \overline{zyx}_6 = 36 z + 6y + x \).

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