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 $$(a+b+c).$$

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