\[ \large \sum_{\text{cyc}(a,b,c)} \dfrac{a^3+b^3}{a+2b} \]

Given that \(a,b\) and \(c\) are positive numbers satisfying \(a^2+b^2+c^2=3\), find the minimum value of the expression above.

Submit your answer to 2 decimal places.

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