You do not need another router. If you run a cable straight to you, you can then plug in an access point.
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You can't have multiple routers like that. If it's rentals, you'd really need to get and pay for your own ISP and then you can register your modem on the coax line. Otherwise you'd need to convince the huge house owner or whoever owns the ISP contract to invest in a better network, whether it's some kind of mesh system or a proper ceiling AP setup.
If your room is setup as an apartment with its own plumbing/cooking, etc. and it has its own official postal address, then you should be able to sign-up for your own personal Internet service.
Otherwise you and the other renters need to get together and have a discussion with the building owner and ask to have better Internet access setup in the whole building.
And the best way to make this happen, is to have someone come in and run dedicated Ethernet cable drops installed to each individual room.