I have tons of experience with this, 2 cats, and I used to travel 60% of the time.
Auto feeders - there are 2 types, gravity (most common) and programmed. Which will work depends on the cat. If you have a cat that doesn't regulate their food and overeats a lot, then a gravity feeder will not work, you'll just end up with a fat cat. Programmed feeders are more expensive, but will put down a specific amount of food on whatever schedule you setup. I use one all the time, and I've found it's reliable as long as I check the batteries and make sure it's full of food. With either type, you're limited to how much food it'll hold.
Water - cats require fresh water. They won't drink (happily at least) from a bowl with stale water. If the cat doesn't drink enough water, then you're risking vet trips for those issues, which aren't cheap. You can get water fountains for pets, and cats often love them (not always of course). Assuming the cat likes the fountain and doesn't dump food in it, you can often leave it unattended for a week or so. Depends on the type of fountain of course, environmental factors, and how much the cat drinks.
The litterbox is also a huge problem. Cats will reach a point where they will refuse to use a dirty box. That point depends on the cat, some are much more tolerant than others. You can alleviate the problem by having multiple boxes, but that only buys you more time, plus a box that hasn't been cleaned in a week is going to smell pretty bad. You entire house will start to smell. Your neighbors may notice and complain, plus once you hit that point the cat is going to kill you.
The bigger problem you can run into is lack of socialization. Cats, despite stereotypes, are social animals and require a certain amount of interaction. How much and what type depend on the cat. Some cats are content to be on their own for a week or more. Others are upset after a day. Some need another cat around to be happy. If you push the limits too far, or too often, there may be a huge backlash.
It's very hard to generalize, because cats are individuals. One of my cats is ok with 4-5 days alone (with another cat for company) for successive weeks, 4-5 months in a row. She's not very happy about it, but she can live with it. I haven't pushed it beyond that. My other cat is a very different matter. She starts acting out, peeing outside the litterbox to express her displeasure, etc. If the pressure doesn't let up (my being out of town), then she will stress herself into a real illness. It happened at least once a year, and the vet trips were not fun.
My solution was to have a pet sitter come in daily to check food and water, clean litterboxes, and pay a little attention to the cats. It wasn't perfect, there were problems, especially long term. But we could limp along until after busy season.