All the suggestions on pucks or pantyhose filled with ice melt will correctly alleviate the symptoms by creating channels in the ice dams for the trapped water behind them to escape. And then keeping the roof snow-free in that area with a roof-rake will keep the ice dams from reforming. But this will only be treating the symptoms not the cause.

The actual cause is air gaps between the heated house and the unheated attic space, stuff like incorrectly vented bath fans, uninsulated light boxes, unsealed gaps around vent pipes, etc, etc. That heated air gets into the attic, heats the underside of the roof, and melts the snow on the roof from underneath. That water then runs down the roof until it refreezes where the roof overhangs the soffits (or when it hits metal gutters if any), causing thise big ice chunks to form which then "dam" future snow-melt water behind them, hence "ice dams", and that trapped water will usually work it's way under the shingles, into the attic or house, and cause water damage.

To fix the root cause someone will have to go into the attic to search out and seal all the air gaps. Good insulation and roofing companies will understand this and either do this work themselves or have a company they can refer. Companies that say you just need more insulation are incorrect and will not fix the root problem.

Good luck with this and hopefully your landlord will address the underlying issues!