Vieta's + Newton's = Trouble

Algebra Level 5

Consider the complex, non-zero, solutions $a, b, c$ and $d$ to

$5x^5+4x^4+3x^3+2x^2+x=0$

If the expression

$\dfrac{ab+ac+ad+bc+bd+cd+abc+abd+acd+bcd+abcd}{a^2+b^2+c^2+d^2-abcd}$

can be written as $-\frac{m}{n}$ , where $m$ and $n$ are positive, coprime, integers, find $m+n$ .

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