About 10 years ago I first had this experience. It was with the Peter Maxwell Davies Trumpet Concerto. I am a trumpeter and at the time I wanted to experience some new music. I started to listen to this work and I could tell there was 'something there' but I could also tell that there was a lot going on in the piece. At first I split it into 5 minute sections and listened to each 5 minute section a few times, then I started listening to the whole thing. It took at least 10 times through before I put it all together and could really enjoy it. It is admittedly a lot of work, and also requires the use of a recording. But I came to realize that complex music can be very enjoyable and I have been something of a new music fan ever since.