Suppose a function $f(x)$ has domain $(-\infty,\infty)$ and range $[-11,3]$. If we define a new function $g(x)$ by $$g(x) = f(6x)+1,$$ then what is the range of $g(x)$? Express your answer in interval notation.

First think I thought of doing was multiplying $-11$ by $6$ and adding $1$ to get $-65$. Then I did the same thing for $3$ to get $19$. I thought the answer was $[-65,19]$. However, this was marked as wrong...Where am I going wrong?