This is why you should be prepared to go the extra mile and try using fax pass-through. It basically makes your VOIP line behave like a normal analogue phone line when it comes to receiving/sending faxes. Note that this will require you to plug your fax machine into your router (if you are using one).
Once these steps are completed, calling your number will activate the fax modem in your voice service provider's demarcation point whereupon it will handshake with the equivalent in your fax machine through which you can finally send the document.
That said, sometimes there may be difficulties in getting ECM working on a VOIP line no matter how hard you try, depending on factors such as network speed, bandwidth usage and the quality of your VOIP service.