A factored polynomial reveals its roots, a key concept in understanding the behavior of these expressions.

If \(a\), \(b\), \(c\), \(d\) and \(e\) are non-negative integers such that

\[x^6-289x^4-x^2+289=(x-a)(x+b)(x-c)(x+d)(x^2+ex+1),\]

what is the value of \(a+b+c+d+e\)?

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