A month may be pushing things as far as fish going without food. I have never used an auto feeder as for some reason or another, have never trusted them.
But as other members says, if you do go this route, do make undoubtly sure teh feeder works correctly EVERY time as I have heard horor stories about food being stuck inside the feeder or the feeder dropping a weeks worth of food in one go and so on and so forth. Check and double check to be 100%.
Personally I have had folks go in my flat and feed my fish once a week for me, I use one of these weekly pill boxes that seals, and just the correct amount for each tank and ask the person to simply add the food content from each relevant box to the relevant tank (which is usually one box per tank and laid next to the tank). And I have a jug that I use strictly for the tanks and ask to top up the water level to the black trim on the tanks (my tanks are open top).
Thats it, never had trouble this way personally. But if am only going away for a week to 10 days, then I simply just do a large water change the day before or on the same day am leaving and ensure fish are fed for at elast 3 days prior to leaving them.
The water change for a month is not worrying me too much as this used to be the normal practice back in the day, yep even routine 2 months water changes was not unheard of! Not recommended now of course as we have learned a lot of things since then.
So a large water change as late as you practically can leave it before you go is good to do and either ensure the auto feeder works 100% each and every time or ask a trusted person to go and feed the fish and top up your tank once a week.