The diagram shows a triangle \(PQR\) in which \(PR=12\text{ cm}\), \(M\) is the mid-point of \(QR\), angle \(PRQ=\dfrac\pi6\) radians and angle \(PQR\) is a right angle.
Without using a calculator, find the value of \(p\) such that angle \(RPM=\sin^{-1}\left(\dfrac{\sqrt p}{14}\right)\).[5]
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