It is possible that at your work, the port 22 is closed, so you cannot go through that port, and not be able to connect to your computer at home. In that case, you should configure your work modem as well to enable that port.
The IP you have to use is your public IP, not the one your modem/router is giving to you (that one is for internal networking). There are numerous websites in internet that will tell you which public IP you have. Also keep in mind that if you have dynamic IP, it will be changing from time to time.
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