Let $m$ be the minimum possible value of, $\log _3\left(3^{y_1}+3^{y_2}+3^{y_3}\right)$ where $y_1, y_2, y_3$ are real numbers for which $y_1+y_2+y_3=9$. Let $M$ be the maximum possible value of $\left(\log _3 x_1+\log _3 x_2+\log _3 x_3\right)$, where $x_1, x_2, x_3$ are positive real numbers for which $x_1+ x_2+x_3=9$. Then the value of $\log _2\left(m^3\right)+\log _3\left(M^2\right)$ is $\_\_\_\_$