Schur

Algebra Level 3

\[\large a^3 + b^3 + c^3 + abc \sqrt5 \] Given that \(a,b\) and \(c\) are the sides of a triangle with perimeter 3. If the minimum value of the expression above can be expressed as \(x + \sqrt y \) for positive integers \(x\) and \(y\), find the value of \(x+ y\).

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