\(\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)=9-4\left(1+\sqrt{2}\right)=5-4\sqrt{2}\)
=> \(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)=25-16.2=-7\)
=> \(x=-7\sqrt[3]{-7}=7\sqrt[3]{7}\)