\(\dfrac{11}{2-\sqrt{3}}+\sqrt{7+4\sqrt{3}}-24\\ =\dfrac{11\left(2+\sqrt{3}\right)}{4-3}+\sqrt{4+4\sqrt{3}+3}-24\\ =\dfrac{22+11\sqrt{3}}{1}+\sqrt{2^2+2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2}-24\\ =22+11\sqrt{3}+\sqrt{\left(2+\sqrt{3}\right)^2}-24\\ =22+11\sqrt{3}+2+\sqrt{3}-24\\ =12\sqrt{3}\)