The following Applipedia screenshot shows the subdivision of LinkedIn Mail from LinkedIn Base, which is the general Application.
If you allow the LinkedIn Base Rule, then succeed it with a new rule of blocking the LinkedIn Mail application (followed by a Commit); this will allow LinkedIn but block the Mail portion of the application.
Note: If using a wild card in your URL filtering profile to match any URL for LinkedIn, the correct syntax is *.linkedin.com, not *linkedin.com.