ĐKXĐ: \(x\ge\dfrac{1}{2}\)
\(\sqrt[3]{x}-1+\sqrt[]{2x-1}-1=0\)
\(\Leftrightarrow\dfrac{x-1}{\sqrt[3]{x^2}+\sqrt[3]{x}+1}+\dfrac{2\left(x-1\right)}{\sqrt[]{2x-1}+1}=0\)
\(\Leftrightarrow\left(x-1\right)\left(\dfrac{1}{\sqrt[3]{x^2}+\sqrt[3]{x}+1}+\dfrac{2}{\sqrt[]{2x-1}+1}\right)=0\)
\(\Leftrightarrow x-1=0\)
\(\Leftrightarrow x=1\)