Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square root equals to the total of the three originals integers. Which of the following best describes the minimum, say m, of these three integers?
- $1 \leq m \leq 3$
- $4 \leq m \leq 6$
- $7 \leq m \leq 9$
- $10 \leq m \leq 12$
- $13 \leq m \leq 15$