Madness continues

Algebra Level 5

(S1+S5)(S1+S9)=(S7+Sa)(S7+Sb)\large(S_1+S_5)(S_1+S_9)=(S_7+S_a)(S_7+S_b)

For Sn=xn+1xnS_n=x^n+\frac{1}{x^n} , if aa and bb are constants that satisfy the equation above, find the value of a+ba+b.

This is one of my original Madness problems.
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