\(\left(7+\sqrt{x}\right)\cdot\left(8-\sqrt{x}\right)=x+11\)

Condition \(x\ge0\)

\(\Leftrightarrow56-7\sqrt{x}+8\sqrt{x}-x=x+11\)

\(\Leftrightarrow-2x+\sqrt{x}+56=11\)

\(\Leftrightarrow-\left(\sqrt{x}-5\right)\cdot\left(2\sqrt{x}+9\right)=0\)

Cause \(x\ge0\Rightarrow2\sqrt{x}+9>0\forall x\ge0\)

So \(\sqrt{x}-5=0\Rightarrow x=25\) (satisfy with condition)

Hence, \(S=\left\{25\right\}\)