jmc

Expanding the left hand side of the given equation, we have $6x^2-17x-45=0$. Since for a quadratic with the equation $a{x}^2+bx+c=0$, the sum of the solutions is $-b/a$, the sum of the solutions of the given equation is $-\frac{-17}{6}=\boxed{\frac{17}{6}}$. (We also could have simply noted that the roots are $-5/3$ and $9/2$, and added these, but who likes adding fractions?)