If you specifically point your like URL fb:like:href="THE URL"
to your Facebook page when you call the AddThis like button it should be in sync with the likes there.
Like so:
<a class="addthis_button_facebook_like" fb:like:href="THE URL TO YOUR FACEBOOK PAGE"></a>
For example:
<a class="addthis_button_facebook_like" fb:like:href="http://www.facebook.com/nike"></a>
Because you reference FB Social Plugins in your tags, I can confirm that this is definitly the case for Facebook's own like button.
<div class="fb-like" data-send="false" data-layout="standard" data-width="450" data-show-faces="false" data-colorscheme="light" data-action="like" data-href="http://www.nike.com/"></div>
gives the likes for that site. And:
<div class="fb-like" data-send="false" data-layout="standard" data-width="450" data-show-faces="false" data-colorscheme="light" data-action="like" data-href="http://www.facebook.com/nike"></div>
Gives the likes displaying for their FB page.