The 100 followers problem!

Algebra Level 5

Given that

\[ \frac{ x}{y} + \frac{ y}{z} + \frac{ z}{x} = 0, \]

the value of

\[\frac{x^{14}z^7+y^{14}x^7+z^{14}y^7}{(x^{10}z^5+y^{10}x^5+z^{10}y^5)(x^{4}z^2+y^{4}x^2+z^{4}y^2)}\]

can be expressed as \( \frac a b \) for coprime positive integers. What is \( a+ b \)?

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