I just did a project chaining 74HCT4040s and it's worked great, as mentioned you just use the output of the highest bit on the first counter into the clock on the next. If you are concerned with current draw, you can buffer the bits before driving your LEDs, but the outputs are plenty for low-brightness LEDs. Also the 74 series chips are usually rated for faster clocks, if that counts for anything in your design. I ran my 74HCT4040s at 32MHz, though there was a different manufacturer that only rated them to 32MHz at 6V. That said, there was a more expensive variant that could go up to 70 or 80MHz.
The one thing to be careful is to be wary of 14 bit counters. Basically, they work fine, but they are put into packages that are too small to break all the outputs out, so generally bits 2 and 3 are missing and are only internal. If you're just concerned with the top end of the count, then it's fine, but if you want the detail in the lower end, there is no way to get that data without another chip or something. No idea why they fit them into the same package as the 12 bit counters, but they did, so if you want every bit exposed, you need to go with a 4040 instead of a 4060.