Let $A$ and $B$ be the two points of intersection of the line $y+5=0$ and the mirror image of the parabola $y^{2}=4 x$ with respect to the line $x+y+4=0$. If d denotes the distance between A and B , and a denotes the area of $\triangle \mathrm{SAB}$, where S is the focus of the parabola $y^{2}=4 x$, then the value of $(a+d)$ is $\_\_\_\_$ .