\(|x^{2018}+|x+1||=x^{2018}+2404\)
\(\Rightarrow x^{2018}+\left|x+1\right|=x^{2018}+2404\)
\(\Rightarrow\left|x+1\right|=2404\)
\(\Rightarrow\orbr{\begin{cases}x+1=2404\\x+1=-2404\end{cases}\Rightarrow}\orbr{\begin{cases}x=2403\\x=-2405\end{cases}}\)