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There is not any simple way to unlock the other part of the safe. It would not be a 'safe' if it were openable without key or combination or both.
While it is true that some cheap safes might be openable by some trick, they are the very cheapest and lowest-quality, and your Brinks safe is not either the cheapest nor the lowest quality.
I suspect you will have to apply to Brinks Security (which may have been acquired by another company name, though offhand I forget which one) with proof of ownership, in order to get another key issued. (If this sounds acceptable as a course to pursue, I will research the true company that now has proprietorship over your Brinks Safe, and let your know what to do.)