Cool Inequality #1 Only AM-GM

Algebra Level 4

\[\frac{a}{b} \ge 3x^{3}y(12-7xy-3x^{2})\]

If \(x,y>0\) and \(a>6,b>1\) and above inequality is satisfied for some co-prime integers \(a\) and \(b\). Find \(a+b\).

Note:- Use only AM-GM to find the answer.

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