\(2x\left(3y-2\right)+\left(3y-2\right)=-20\)
\(\Rightarrow\left(2x+1\right)\left(3y-2\right)=-20\)
\(\Rightarrow\left(2x+1\right);\left(3y-2\right)\in U\left(20\right)=\left\{-1;1;-2;2;-4;4;-5;5;-10;10;-20;20\right\}\)
\(\Rightarrow\left(x;y\right)=\left(0;-6\right);\left(-3;2\right);\left(2;0\right)\)
\(\Rightarrow\left(x+y\right)_{max}=2+0=2\)