\(=\lim\limits_{x\rightarrow0}\dfrac{\sqrt[3]{x+1}\left(\sqrt[]{2022x^2+x+1}-1\right)+\sqrt[3]{x+1}-1}{x}\)
\(=\lim\limits_{x\rightarrow0}\dfrac{\dfrac{\sqrt[3]{x+1}.\left(2022x^2+x\right)}{\sqrt[]{2022x^2+x+1}+1}+\dfrac{x}{\sqrt[3]{\left(x+1\right)^2}+\sqrt[3]{x+1}+1}}{x}\)
\(=\lim\limits_{x\rightarrow0}\left(\dfrac{\sqrt[3]{x+1}\left(2022x+1\right)}{\sqrt[]{2022x^2+x+1}+1}+\dfrac{1}{\sqrt[3]{\left(x+1\right)^2}+\sqrt[3]{x+1}+1}\right)\)
\(=\dfrac{1}{1+1}+\dfrac{1}{1+1+1}=\dfrac{1}{2}+\dfrac{1}{3}=\dfrac{5}{6}\)
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