Restore the last full backup
Restore the 1pm differential
Restore all the log backups since that diff.
Whether or not you can recover that 55 minutes since the last log backup depends on the type of failure. Look in books Online for the discussion of 'Tail-log backup'
That risk is why the log backup interval should be less than the allowable data loss for the system.
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)SQL In The Wild
: Discussions on DB performance with occasional diversions into recoverability
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