Madness continues

Algebra Level 5

$\large(S_1+S_5)(S_1+S_9)=(S_7+S_a)(S_7+S_b)$

For $S_n=x^n+\frac{1}{x^n}$ , if $a$ and $b$ are constants that satisfy the equation above, find the value of $a+b$ .

This is one of my original Madness problems.