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Last Tested: Sep 6, 2019
You can find the merged query id after the mid= in the url!
For example, in this URL, https://master.dev.looker.com/merge?mid=5Pu6Q0FUz4ESXM23DwUQOi&toggle=vis, the merged query id is 5Pu6Q0FUz4ESXM23DwUQOi.
Note: it's not currently possible to run merged queries via the API.