A parallelogram of length \(AB\) \((\sqrt{6}-1)\) cm has an area of \((2\sqrt{6}+3)\) cm\(^2\).
Without using a calculator, find the perpendicular height, \(h\), in the form \((a+b\sqrt{6})\) cm, where \(a\) and \(b\) are integers.[3]
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