\(\displaystyle \int\frac{7x^{13}+5x^{15}}{\left(x^7+x^2+1\right)^3}dx = \frac{1}{a}\cdot \frac{x^{b}}{\left(x^7+x^2+1\right)^c}\)

Given that the indefinite integral above is true, then what is the value of \( a+b+c, \) where \(a,b,\text{ and }c\) are positive integers?

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