\(\Leftrightarrow\left(\sqrt[3]{2x-1}+\sqrt[3]{2x+1}\right)^3=10x\)
\(\Leftrightarrow2x-1+2x+1+3\left(\sqrt[3]{2x-1}\right)^2\sqrt[3]{2x+1}+3\sqrt[3]{2x-1}\left(\sqrt[3]{2x+1}\right)^2=10x\)
\(\Leftrightarrow3\left(\sqrt[3]{2x-1}\right)^2\sqrt[3]{2x+1}+3\sqrt[3]{2x-1}\left(\sqrt[3]{2x+1}\right)^2=6x\)
\(\Leftrightarrow\sqrt[3]{2x-1}.\sqrt[3]{2x+1}.\left(\sqrt[3]{2x-1}+\sqrt[3]{2x+1}\right)=2x\)
\(\Leftrightarrow\sqrt[3]{4x^2-1}.\sqrt[3]{10x}=2x\)
\(\Leftrightarrow\left(\sqrt[3]{4x^2-1}.\sqrt[3]{10x}\right)^3=8x^3\)
\(\Leftrightarrow10x\left(4x^2-1\right)=8x^3\)
\(\Leftrightarrow40x^3-10x=8x^3\)
\(\Leftrightarrow32x^3-10x=0\)
\(\Leftrightarrow2x\left(16x^2-5\right)=0\)
\(\Leftrightarrow2x\left(4x-\sqrt{5}\right)\left(4x+\sqrt{5}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{\sqrt{5}}{4}\\x=-\dfrac{\sqrt{5}}{4}\end{matrix}\right.\)
