One of the shortlisted problem of I.M.O

Algebra Level 3

Let a, b and c be positive real numbers such that $abc = 1$ than find the maximum value of $$\frac{ab}{a^5+b^5+ab}+\frac{bc}{b^5+c^5+bc}+\frac{ca}{c^5+a^5+ca}$$

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