I don't see it in the docs, but I've found several things that are inconsistent with the docs, for instance removing a blog entry can only be done with removePage, rather than the documented removeBlogEntry method.
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I think you need to do this using the REST API from the Like plugin. The Like plugin's REST API is accessible @ ${confluence.url}/rest/likes/1.0/content
For example, a POST to http://localhost:1990/confluence/rest/likes/1.0/content/123456/likes
Would add a new Like for the current user on the page that has an ID of 123456
You can use the REST API Browser included in the Atlassian Plugin SDK to browse the available functionality of the API.
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