It's rare that someone comes on here and gets told to bring *more* stuff rather than less, but here we are. I've used rental bikes with a single 60 liter bag tied on back, and it's been clumsy but do-able. I haven't done this with camping gear included, because carrying a tent, sleeping bag, sleeping pad, stove, cookware, additional food and water, and random other items would require a bigger (or second) bag. Whatever you decide, bring a couple of extra straps and/or (my favorite) heavy rubber bungie cords.

The comments interspersed in previous posts are worth careful consideration--for example, you'll need a way to secure your riding jacket, pants, boots, helmet, and gloves while away from the bike. Depending on where you're headed, this might be as simple as a lightweight cable and an unappealing nylon cover. You should at least consider a secure lock for the bike, too. You'll need to carry some food and water, a change of footwear, spare clothes (including waterproofs and warm layers), toiletries, any electronics, probably a few parts and tools (at least a tire kit, something for lubing and adjusting chains, a way of tightening the stuff that otherwise vibrates loose and falls off, etc.), a basic first aid kit....

If the concept of earplugs--pretty basic, IMO-- is new to you, probably it'll be worth consulting any of the endless lists people post all over the internet, because chances are pretty good there's more you're missing. On the other hand lots of people carry absurd amounts, and you're just going for a month during late summer, a pretty friendly season.

Hope that's helpful!

Mark