6. Let real numbers $x, y$ satisfy $\left\{\begin{array}{l}x^{3}-3 x^{2}+2026 x=2023, \\ y^{3}+6 y^{2}+2035 y=-4053,\end{array}\right.$ then $x+y=$
$$
\begin{array}{l}
\left\{\begin{array} { l } 
{ x ^ { 3 } - 3 x ^ { 2 } + 2026 x = 2023 , } \\
{ y ^ { 3 } + 6 y ^ { 2 } + 2035 y = -4053 }
\end{array} \Rightarrow \left\{\begin{array}{l}
(x-1)^{3}+2023(x-1)=-1 \\
(y+2)^{3}+2023(y+2)=1
\end{array}\right.\right. \\
\Rightarrow x-1=-(y+2) \Rightarrow x+y=-1
\end{array}
$$