\(z=\frac{\sqrt[3]{9\sqrt{3}+11\sqrt{2}}+\sqrt[3]{9\sqrt{3}-11\sqrt{2}}}{2}\)
= \(\frac{\sqrt[3]{3\sqrt{3}+9\sqrt{2}+6\sqrt{3}+2\sqrt{2}}+\sqrt[3]{3\sqrt{3}-9\sqrt{2}+6\sqrt{3}-2\sqrt{2}}}{2}\)
= \(\frac{\sqrt[3]{\left(\sqrt{3}+\sqrt{2}\right)^3}+\sqrt[3]{\left(\sqrt{3}-\sqrt{2}\right)^3}}{2}\)
= \(\frac{\sqrt{3}+\sqrt{2}+\sqrt{3}-\sqrt{2}}{2}\) = \(\frac{2\sqrt{3}}{2}=\sqrt{3}\)