What is the sum of the 4-digit Babylonian narcissistic numbers?

This problem's question is: What is the sum of the 4-digit Babylonian narcissistic numbers?

A narcissistic number is a number in the specified base (the default is base 10) whose length without leading zeroes in the base is the power to which its non-zero digits are raised and then the powers summed and if that sum is the original number, then the number is narcissistic.

For the purposes of this problem, a Babylonian number simply means that its representation is base 60.

For example, a three digit decimal (base 10) number, 153 is narcissistic: $1^3+5^3+3^3=1+125+27=153$ .

To help you, the four digit Bablylonian numbers have decimal values between $216\,000$ and $12\,959\,999$ .