jmc

If Eleanor made $N$ cookies, we know from the first requirement that $N=11x+4$ for some integer $x,$ and from the second requirement we know that $N=7y+1$ for some integer $y.$ Therefore, $$11x+4=7y+1\Rightarrow 11x+3=7y$$If we list the possible values of $11x+3$ such that $N=11x+4<100,$ we have $14,$ $25,$ $36,$ $47,$ $58,$ $69,$ $80,$ $91.$ The only members of this list divisible by $7$ are $14$ and $91,$ and so the possible values of $$11x+4=7y+1$$are $14+1=15$ and $91+1=92$, and thus the sum of the possible numbers of cookies is $15+92=\boxed{107}.$