Complex Cyclic Cystems

Algebra Level pending

Let \(a,b,c\) be non-zero complex numbers such that \[\frac{2b+3c}{a}=\frac{2c+3a}{b}=\frac{2a+3b}{c}.\] Find the sum of all (distinct) possible values of \(\left|\frac{5b^2+5c^2}{a^2}\right| \).

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