Đặt \(x=\sqrt[3]{9+4\sqrt{5}}+\sqrt[3]{9-4\sqrt{5}}\)
\(\Rightarrow x^3=18+3x.\sqrt[3]{\left(9+4\sqrt{5}\right)\left(9-4\sqrt{5}\right)}\)
\(\Leftrightarrow x^3=18+3x\)
\(\Leftrightarrow x^3-3x-18=0\)
\(\Leftrightarrow\left(x-3\right)\left(x^2+3x+6\right)=0\)
\(\Leftrightarrow x=3\)