Calculus · Hard problem

A reliability model's density is proportional to $g_n(x)=x(1-x)^n$ on $[0,1]$, for a positive integer $n$. Substituting $u=1-x$ shows that its normalizing integral is $\displaystyle\int_0^1x(1-x)^n\,dx=\dfrac1{(n+1)(n+2)}$. For what value of $n$ does this normalizing integral equal exactly $\dfrac1{110}$?