We complete the square for both $x$ and $y$ by adding the square of half the coefficient of the linear term:
$x^2+2x+y^2+10y=-16 \Rightarrow (x+1)^2-1+(y+5)^2-25=-16 \\
\Rightarrow (x+1)^2+(y+5)^2=8$
This equation represents a circle centered at $(-1,-5)$ with radius $\sqrt{8}=2\sqrt{2}$
The sum of the coordinates of the center is $(-1)+(-5)=\boxed{-6}$
The answer is: -6
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The center of the circle with equation $x^2+y^2=-2x-10y-16$ is the point $(x,y)$. What is $x+y$?

### Answer:
