The right frequency depends more on your water conditions than on a fixed rule, so once a month is a good starting point but maybe not for everyone. What really matters is how dirty the filter gets: if you see the water flowing less well or you notice food residue floating around, then it's time to clean it, regardless of how many days have passed. Yeah, the type of fish and especially how much they eat make a difference - a tank with fish that produce a lot of waste will need more frequent cleanings than one with tidier species.
The practical tip is to check the filter every 2 - 3 weeks without necessarily cleaning it each time, so you get a feel for your tank's rhythm. A lot of people make the mistake of cleaning too often: the filter thrives on good bacteria that break down waste, and if you give it a thorough wash every week you kill them off. Better to do a light rinse in tank water (not tap water, which kills the bacteria) rather than a full cleaning.
For a 60-liter tank like yours, I'd say go like this: visually check every 3 weeks, do a light rinse if needed, and a more thorough cleaning maybe every 4 - 6 weeks if things are going well. If you notice your parameters going haywire or the water smells off, bump up the frequency. Every tank is different, so listen to yours instead of fixating on dates.