This is a known issue that can impact the move and delete functionality just after upgrade to 6.5 service pack 11. It has been detailed in SP 11 release notes as well. The issue occurs as the background query fails while trying to fetch Content Fragment references.
When trying to move/delete/publish either Content Fragments or Sites/Pages, there is an issue when Content Fragment references are fetched, as the background query fails and the functionality does not work.
Please refer Known issues section release notes for the same.
To ensure correct operation you need to add the following properties to the index definition node /oak:index/damAssetLucene (no re-indexing is required)
To fix this issue a property must be added to /oak:index/damAssetLucene to set the index tag used by the affected query, so it will use this index when executing said query.
1 - Enable CRX/DE (if not already enabled)
2 - Open CRX/DE and navigate to /oak:index/damAssetLucene
3 - Add a property:
4 - Add another property:
5 - Once the properties have been added, save your changes