Underneath the radar is spot on. Let them know you're coming. I don't work the MNG airspace but do the other two sectors between 30 and 100nm ML. ie from the north anticlockwise round to the southeast.
Always have a plan in and call early, not at 5 nm from the cta step. Get your code, get identified, let arrivals do a bit of planning. The process often involves you calling enroute, enroute talking to ML radar and possibly flow, Radar checking with Departures/Arrivals. It all takes time. Most of the guys will do everything possible to get you through but some days it just doesn't work.