A thin rectangular plate of length \(L\) and width \(W\) lies in the \(xy\)-plane bounded by \(x = 0\) to \(x = L\) and \(y = 0\) to \(y = W\). The surface mass density of the plate is non-uniform and given by \(\sigma(x) = \sigma_0 \left(\dfrac{x}{L}\right)^2\), where \(\sigma_0\) is a constant. What is the \(x\)-coordinate of the center of mass of the plate?