The diagram shows the curve \(y=1+x+5\sqrt{x}\) and the straight line \(y-3x=3\). The curve and line intersect at the points \(A\) and \(B\). The lines \(BC\) and \(AD\) are perpendicular to the \(x\)-axis.

(i) Using the substitution \(u^2=x\), or otherwise, find the coordinates of \(A\) and of \(B\). You must show all your working.

(ii) Find the area of the shaded region, showing all your working.