In the diagram, \(ABCD\) is a trapezium. \(AB\) is parallel to \(DC\), \(AB=\left( x+4 \right)\) cm, \(DC=\left( 3x+1 \right)\) cm and the height is \(12\) cm. Given that the area of the trapezium is \(114\) cm\({^2}\), find the value of \(x\).

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