Side lengths of a triangle with a 120 degree angle from algebraic sides, its area and a sum of sines

In triangle \(PQR\), \(QR=x\text{ cm}\), \(PR=(x+1)\text{ cm}\) and \(PQ=(2x-1)\text{ cm}\), where \(x>2\). The largest angle of the triangle is \(120^\circ\).

1. Find the value of \(x\).[4]
2. Show that the area of triangle \(PQR\) is \(14\sqrt3\text{ cm}^2\).[2]
3. Find the exact value of \(\sin P+\sin Q+\sin R\), giving your answer in the form \(\frac{a\sqrt b}{c}\), where \(a\), \(b\) and \(c\) are positive integers.[3]