Madness-4

Algebra Level 5

Let \(S_n=(x^n+\frac{1}{x^n}).\)

Now \[(S_3+S_1)(S_7+S_1)(S_{11}+S_1)=(S_a+S_7)(S_b+S_7)(S_c+S_7)\]

If the equation above is always true then find the value of \((a+b+c).\)

This is one of my original Madness problems.
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