Syljun,
The Findmypast record can be found within the Marriage Records by searching for John Hadden b. 1700 d. 1740. There are 3 records returned with this search within the Parish Records Collection, Marriages and the one for 1740 is the record of the Faculty Office Marriage Licence Allegations 1701-1850 that are held on Microfiche by the Society of Genealogists. The transcript on findmypast won't give you any more than I have already provided, but there may be more available on the scan of the actual document.
SoG also hold (as part of the same series) the Vicar-General Marriage Licence Allegations 1694-1850 and the same search returns a record from 12 Sep 1739 between a Dingley and a Hadden, but there are no first names. This could also be for the same couple, but because it is National it might not be; you can't tell without looking. I believe that, depending on the circumstances as to why a Licence was being applied for, the originals can contain information on the Parish of origin of the couples, names of guarantors, ages of the parties (at least over 21), and a signature of the applicant but equally it may not add much more than you have from the register.
Last time I needed one, the records could be obtained by visiting SoG in person in London (members free, but you can purchase a Visitors Pass) and paying a pound for a print of the fiche; or by paying £10 on-line and having the scan posted out to you. This option may only be available through the link on findmypast. However, SoG are very helpful if you send them an e-mail, or give them a call.
As an aside, I would also look at the names of the other Dingleys that seem to have married in Bridgewater around the same time, that can be found on IGI. They may lead you somewhere, if they are siblings.
Neil