Unclogging HVAC line at the plenum

OK, I'm new at this, but am trying to avoid a call to the AC guy that my husband thinks I should make. Our upstairs AC line appears to be clogged between the plenum and the drain. The water is dripping into the overflow. We ran a snake into the drain at the overflow, and that section is not clogged. Can we safely access the drain at the plenum and unclog this ourselves without damaging the plenum or drain? A quick response would be great, or I have to call for service! Thanks.