I always seem to have problems installing Dropbox using the versions available in the software manager (even when I select the one for Mint’s file manager). When I start Dropbox from the menu there is no GUI presented and no icon in the taskbar. However you can see that a process is running:
    # ps -A | grep drop
It turns out this is probably somethng to do with a corupt install or the version in Software Manager being outdated.
To fix this we need to clear the Dropbox folders from our home folder:
    # cd ~
    # rm -rf .dropbox*
The next thing we want to do is install the latest version of Dropbox. To do this go to https://www.dropbox.com/install?os=linux and scroll to the section “Install Dropbox via Command Line”. At the time of writing these were the commands for the latest version:

    cd ~ && wget -O – “https://www.dropbox.com/download?plat=lnx.x86” | tar xzf –
    cd ~ && wget -O – “https://www.dropbox.com/download?plat=lnx.x86_64” | tar xzf –

You can then start dropbox from the icon in the OS menu.