\(PT\Leftrightarrow\left(\sqrt[3]{x+1}+1\right)+\sqrt[3]{x+2}+\left(\sqrt[3]{x+3}-1\right)=0\\ \Leftrightarrow\dfrac{x+2}{\sqrt[3]{\left(x+1\right)^2}-\sqrt[3]{x+1}+1}+\dfrac{x+2}{\sqrt[3]{\left(x+2\right)^2}}+\dfrac{x+2}{\sqrt[3]{\left(x+3\right)^2}+\sqrt[3]{x+3}+1}=0\\ \Leftrightarrow\left(x+2\right)\left(\dfrac{1}{\sqrt[3]{\left(x+1\right)^2}-\sqrt[3]{x+1}+1}+\dfrac{1}{\sqrt[3]{\left(x+2\right)^2}}+\dfrac{1}{\sqrt[3]{\left(x+3\right)^2}+\sqrt[3]{x+1}+1}\right)=0\)
Dễ thấy ngoặc lớn luôn khác 0
\(\Leftrightarrow x=-2\)