It used to say "by 11:59 pm" on the
Disneyland website, but they removed that language several years ago. More recently, when I asked, I got several different answer depending on the CM I spoke with, so I don't think anyone really knows for sure. I've been told that "one day" could mean:
1) by 11:59 pm the day before the reservation (e.g., so by 11:59 pm on Monday for a Tuesday reservation),
2) 24-hours before the reservation (e.g., so by 11:30 am on Monday for a 11:30 am Tuesday reservation), or
3) a full day before (e.g., so by 11:59 pm Sunday for a Tuesday reservation)
I think it mostly likely means either anytime the day before, but to be safe, I would try to cancel at least 24-hours in advance.