Hi Iris,
I would agree with Okaydaniel - It does include having no manners, but it also means people who are uncultured - so people who don't know much about art and music, which implies a poor education. However, I don't see a connection between 'uncultivated' and 'uncaring'.
In my opinion, you could refer to teenagers who play video games all day long, as uncultivated (since, if all you do is play video games, there is no time left to cultivate yourself). However, playing video games doesn't necessarily exclude cultural knowledge, and it would make more sense to use this word to refer to people who have never heard of Shakespeare, or who don't like reading, going to the theatre, or listening to classical music.
HTH
Rachel