Adding a service "linkedin" from the sharethis settings page:
[+] Click to change order of social buttons or modify list of buttons. (?)
should add the linkedin button to your blog. Can you please make sure that the changes you make from sharethis configuration page get saved for your wordpress blog?
If the changes aren't getting saved,then it can be because of sharethis plugin incompatibility with any of the plugins you're using for your blog.
Can you please retry changing the sharethis settings by disabling the other plugins ?If it still doesn't work for you then you can add the buttons manually to your wordpress blog.
Please let us know if you want the steps to add the buttons manually.
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