Very nice find (1756 is correct). Mexico City stopped producing hand-struck cobs in 1733.
In 1733, still cutting irregular blanks by hand, Mexico pressed the blanks between a screw press, rather than hand-striking the coins. These are called "klippes", & were struck for 2 years, in 1733 & 1734.
The above design, your coin, (known as "pillar dollars"), was first struck in 1735. Mexico used round, uniformly cut blanks that were struck in a screw press, with a collar around the edge. the collars served to keep the round shape, as well as impressing a design onto the edge. The edge design discouraged the practice of drilling into & removing silver from the coins This design continued at Mexico City until 1772, when it was abandoned for the King's portrait.
The below shows the evolution from (hand-struck) cobs to machine milled coins: