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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