jmc

Both sides of this equation can be simplified using the Binomial Theorem. Note that $-729=(-9{)}^3$, $25=5^2$, and $9=3^2$. This gives us ${\left(\frac{x}{3}-9\right)}^3=(5+3{)}^2=8^2=64$, so $\frac{x}{3}-9=4$. Therefore, $x=3(4+9)=\boxed{39}$.