Not as complicated as it look

Algebra Level 3

\[ x^9 - x^7 - x^6 - x^5 + x^4 + x^3 + x^2- 1 \]

Given that the above expression completely factors to \( (x+a)^b (x+c)^d (x^d + c)(x^d + x+ c) \) for integers \(a,b,c,d\), find \(a+b+c+d\).

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