Distances along meridians are equal at all points - 1 minute of arc is equal to 1 NM at all points along a meridian. This is true of ALL meridians.

However, 1 minute of arc measures differing distances on different line of latitude.

For arguments sake, let's also say that 1' of arc at the Equator measures 1 NM, which is what we assume for practical reasons. As shown in my earlier answer the difference is so small (0.001 NM or 6.08 ft), it is academic and not considered practically.

However, North and South of the Equator the meridians converge, therefore, 360º at the Equator (21,600 NM) is a greater distance than 360º at any other latitude.

This is calculated using the Departure Formula, as follows:

Departure = Change of Longitude (minutes of arc) x Cosine of the Latitude
Departure = (360º x 60') x Cosine 45º
Departure = 21,600' x 0.707
Departure = 15,273.5 NM

Look at 1 minute of arc at the Equator, using the same formula:

Departure = Change of Longitude (minutes of arc) x Cosine of the Latitude
Departure = 1' x Cosine 0º
Departure = 1' x 1
Departure = 1 NM

Now look at 1 minute of arc at 45ºN:

Departure = Change of Longitude (minutes of arc) x Cosine of the Latitude
Departure = 1' x Cosine 45º
Departure = 1' x 0.707
Departure = 0.707 NM