\(x=\sqrt[3]{2}+\sqrt[3]{4}\)
=>\(x^3=\left(\sqrt[3]{2}+\sqrt[3]{4}\right)^3=6+3\cdot\sqrt[3]{2}\cdot\sqrt[3]{4}\left(\sqrt[3]{2}+\sqrt[3]{4}\right)\)
=>\(x^3=6+3\cdot2\cdot x\)
=>\(x^3-6x-6=0\)
\(A=\sqrt{x^5-5x^3-6x^2-6x+3}\)
\(=\sqrt{x^5-6x^3-6x^2+x^3-6x-6+9}\)
\(=\sqrt{x^2\left(x^3-6x-6\right)+\left(x^3-6x-6\right)+9}\)
\(=\sqrt{0\cdot x^2+0+9}\)
\(=\sqrt{9}=3\)