jmc

Completing the square, we add $(12/2{)}^2=36$ to both sides of the equation to get $x^2+12x+36=109\Rightarrow (x+6{)}^2=109$. Taking the square root of both sides, we get $x+6=\sqrt{109}$ (we take the positive square root because we want the positive solution), or $x=\sqrt{109}-6$. Thus, $a=109$ and $b=6$, so $a+b=\boxed{115}$.