Upvote:2
If everything on the passport is clearly readable then you will probably be OK. If any part is unreadable then you should get a new one. Most countries allow you to do a passport renewal in well under a month.
If you have time to get a new passport I would still recommend getting a new one, even if everything is readable. The likelihood is that it will be accepted. Much worse things happen to passports on long trips, and I used a water-damaged passport for several year. However the downside of getting an exceptionally strict immigration officer and being refused entry is much more serious than the cost of a new passport.