I have a 1967 coupe barracuda with a low serial number and shipped march 1966.

Despite mis information on the internet VIN numbers did not exist prior to 1969. Those earlier cars had simple serial numbers.

No, they had actual, real VINs (which means "vehicle identification number", so there's no need to say "number" again). Take a look:

LH41B62123456
LH41B9B123456
LH41C2B123456

Those are '66, '69, and '72 Dart high-trim 4-door sedans built at Hamtramck with 225 engines, each with the serial number 123,456. So where's any of your claimed pre/post '69 difference?

And we don't even have to stop at '66; let's go back further:

7342567890 - '65 Dart 270 built at Detroit, serial number 567,890.

7325123456 - '62 Lancer 770 built at Los Angeles, serial number 123,456.

1709123456 - '60 Valiant V-200 station wagon built at Windsor, serial number 123,456

In all three of these pre-'66 cases the first four digits aren't serial, they're assigned meanings just like the first seven characters of a '66-up VIN.

Take a look here. VINs in the North American market were not standardised until 1981 when the present 17-character system came into effect. Prior to that, all manufacturers picked their own format and number of characters.

(since we're talking about misinformation on the internet and all that…)