Okay, that was a shot in the dark..................it only works sometimes if there is an uninstall rule provided by the developers.....
But qt is easy to remove since it installs itself into one directory............look for either /usr/lib/qt-<version> or /usr/local/lib/qt-<version> and delete that directory............There might be a qt directory in /usr/doc or /usr/local/doc but the main directory is in one of the lib directories........
HTH
PS: The directory might just be named qt without the version number attached........