searching for radio-stations
The default Rhythmbox URL based radio-station capability is limited - you have to research the internet radio-station - and then find what the actual URL it uses to play the radio-stream.
Fortunately - there is another way
disclaimer - I'm the author of this plugin
The RadioBrowser plugin could be useful if you like to browse for new radio stations.
You mentioned Jazz...
There are several jazz radio-stations as shown in the picture.
More information in the links below
sudo add-apt-repository ppa:fossfreedom/rhythmbox-plugins
sudo apt-get update
sudo apt-get install rhythmbox-plugin-radio-browser
then start rhythmbox and select the menu edit-plugins, tick the checkbox internet radio station browser