I believe it is generally against code to have low-voltage wire running through the same passage as 120/240v, but I am not 100% sure on this. Only an inspector would be for sure for your area... My experience with an inspection was this (for my area)
1 foot sepration was preferred, but not required for wall outlets; data/coax next to electrical (I see many that are closer)
should not go through the same pass-thru on wood studs (again 1 foot seperation, more if it was a metal stud)
if needed to go to a second story, conduit was preferred with caulk fire-stop required (really had no way to check this without damage to installation)
absolutly no if they go through the same conduit.
Now you may ask 1 foot sepration seems kind of excessive... I asked too. I was told that it was just a recommendation, but code was actually only something like 2-4 inches.
My personal experience is never run data/comm cabling parrallel within 1 foot to any 120+ voltage lines, perpendicular is ok, just not parrallel. YMMV.
That all being said, if you know where the 110 is going through, you could easily measure and find the next wall cavity over and make a new hole.
Is your house 1 story? Basement? etc
Others here might have more exact numbers, I am just going by what I remember when we did some inspections on homes we were looking at buying