Correct. If $\displaystyle{3}{\sqrt[{{5}}]{{{x}+{3}}}}+{4}={\sqrt[{{5}}]{{{x}+{3}}}}\usepackage{cmbright}\Huge\$ , then $\displaystyle{2}{\sqrt[{{5}}]{{{x}+{3}}}}=-{4}\usepackage{cmbright}\Huge\$ , so $\displaystyle{\sqrt[{{5}}]{{{x}+{3}}}}=-{2}\usepackage{cmbright}\Huge\$ . $\displaystyle{{\left({\sqrt[{{5}}]{{{x}+{3}}}}\right)}}^{{5}}={{\left(-{2}\right)}}^{{5}}=-{32}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}+{3}=-{32}\usepackage{cmbright}\Huge\$ . Therefore, $\displaystyle{x}=-{35}\usepackage{cmbright}\Huge\$ .