We know \(a=\sqrt{11}+\sqrt{13},b=\sqrt{11}+2\sqrt{13}\) and \(c=\sqrt{11}+3\sqrt{13}\) The expression \(a^2(b-c)+b^2(c-a)+c^2(a-b)\)evaluates to a number which can be written in the form \(p\sqrt{q}\) for integers p and q, where q is square-free. Find p+q.
