Sixth Power as Sum of 7 Sixth Powers

Theorem
The smallest known integer whose $6$th power can be expressed as the sum of $7$ smaller $6$th powers is $1141$:


 * $1141^6 = 74^6 + 234^6 + 402^6 + 474^6 + 702^6 + 894^6 + 1077^6$