Let a, a + 1, a + 2, ... , a + 10 be the integers. We have :

\(a+\left(a+1\right)+\left(a+2\right)+...+\left(a+10\right)=11\)

\(\Leftrightarrow11a+\dfrac{10.11}{2}=11\Leftrightarrow a+\dfrac{10}{2}=1\Leftrightarrow a=-4\)

So, the answer is -4