I added a minisplit last year for cooling and heating. I was worried about dust, especially when I am turning or using my CNC so I bought a couple of Merv 11 filters that I put over the intake to help catch the airborne dust before it gets inside the MS. This was a my first prototype where I cut and adapted a larger filter but it shows the general idea.
The blue pieces of foam act as springs to hold it tight and prevent air from sneaking in around the filter. I also usually put some gaffers or masking tape around the cover to seal the cabinet better so that all of the air goes through the filter. I have checked the internal air filter (more of a screen) about 3 times and it has not had any dust on it and I can see no fine dust on the coils. The filter does lower the air flow slightly when measured with an anemometer but it does not seem to affect cooling or heating performance that I can tell.
I also have a Wen air cleaner similar to Dave's but I wasn't really happy with how loud it is so I made a DIY air cleaner that works much better than the Wen to remove as much of the dust out of the air as possible before it can get into the minisplit. I wrote about my experimentation here.
--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.