Sound Insulation- how much can it help?

I am considering moving into a new apartment, but the neighbor's (with yound child) bedroom is right next to my living room. I want to listen to music and watch movies at fairly loud volume late at night. At a volume that was way too low for me, i.e. I need it 3-4 times louder at a minimum), they asked me to turn it down another half. We have concrete walls, and with a fairly large (5 meters long and 5 meters high- vaulted ceiling) shared surface area. Is there any soundproofing method that can work? How much sound can be reduced? At what volume will I be able to play my music any time of day or night?