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:


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

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.