jmc

We complete the square for the equation by observing that the given equation is equivalent to $$(x^2+6x+9)+(y^2+8y+16)=25,$$ so the equation for the circle becomes $$(x+3{)}^2+(y+4{)}^2=5^2.$$ Hence, the center is $(-3,-4)$ which implies that the answer is $-3-4=\boxed{-7}$.