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Consider the complex, non-zero, solutions a,b,ca, b, ca,b,c and ddd to
5x5+4x4+3x3+2x2+x=05x^5+4x^4+3x^3+2x^2+x=05x5+4x4+3x3+2x2+x=0
If the expression
ab+ac+ad+bc+bd+cd+abc+abd+acd+bcd+abcda2+b2+c2+d2−abcd\dfrac{ab+ac+ad+bc+bd+cd+abc+abd+acd+bcd+abcd}{a^2+b^2+c^2+d^2-abcd}a2+b2+c2+d2−abcdab+ac+ad+bc+bd+cd+abc+abd+acd+bcd+abcd
can be written as −mn-\frac{m}{n}−nm, where mmm and nnn are positive, coprime, integers, find m+nm+nm+n.
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