Set of 5 Triplets whose Sums and Products are Equal

Theorem
The following set of $5$ triplets of integers have the property that:
 * the sum of the integers in each triplet are equal

and:
 * the product of the integers in each triplet are equal:


 * $\tuple {6, 480, 495}$, $\tuple {11, 160, 810}$, $\tuple {12, 144, 825}$, $\tuple {20, 81, 880}$, $\tuple {33, 48, 900}$

The sum is $981$, and the product is $1 \, 425 \, 600$.

This is the only known such set of $5$ triplets of integers with this property.