On Ubuntu you need libreadline6 and libreadline6-dev, though I don't know whether that is the same on mint. You might need to remove and re-install ruby in rvm after installing libreadline so that it re-compiles with the right options. The full list of stuff I install before installing rvm is sudo apt-get install build-essential bison openssl libreadline6 libreadline6-dev curl git-core \ zlib1g zlib1g-dev libssl-dev libyaml-dev libxml2-dev autoconf libc6-dev ncurses-dev automake \ libtool
By the way, when you get an error you don't understand often the best route is to put the error message into google. I think that would have taken you to a solution very quickly.
Colin