Hey Jakob,
Just to get back to your original issue, depending on the version of X that is active on your site, it will automatically install Cornerstone as soon as you login to the Wordpress dashboard.
Also, since your site has X active on it, you will not able able to use the Cornerstone license to validate X. You will have to use another theme and validate Cornerstone using the license that you have.
At this point, what you can do is to download the latest version of Cornerstone from your Apex dashboard.

Once downloaded, unzip the file and you should have a cornerstone folder which the plugin files in it. Login to FTP and go to wp-content/plugins then delete the current cornerstone directory that is in there. Once deleted, upload the unzip cornerstone directory that you have just downloaded from apex.
Once all files are uploaded, go back to the Wordpress admin and you should have the latest version of Cornerstone on your site.
Hope this helps.