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.
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