Base of number base

Number Theory Level 2

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 $\overline{zyx}_6 = 36 z + 6y + x$ .