An algebra problem by Phudish Prateepamornkul

$\begin{cases} a^{3} b^{2}+b^{3} c^{2}+c^{3}a^{2} = \dfrac{103}{1024} \\ a^{2} b^{3}+b^{2}c^{3}+c^{2}a^{3} = \dfrac{125}{1024} \\ a^{2} b^{2} c+a^{2} b c^{2}+a b^{2}c^{2} = \dfrac{33}{512}\end{cases}$

Let reals $a$ , $b$ and $c$ satisfy the system of equations above. If $\dfrac{a-b}{c}+\dfrac{b-c}{a}+\dfrac{c-a}{b} = - \dfrac{x}{y}$ , where $x$ and $y$ are coprime positive integers, find $x+y$ .