In order to solve this equation, we will simplify the equation by changing the denominator of all fractional terms into their least common multiple.

First, we need to find the least common multiple of 15, 12 and 10. Their least common multiple is 60. Therefore, we change the denominator of each score to 60 and get:

4x ÷ 60 + 5x ÷ 60 + 6x ÷ 60 = 1365

Now, we can remove the denominator of the fractional terms and add up the molecules of each fractional term to get:

(4x + 5x + 6x) ÷ 60 = 1365

Add up the molecules to get:

15x ÷ 60 = 1365

Continue to simplify:

15x = 1365 × 60

Now, calculate the product on the right side of the equation and get:

x = ( 1365 × 60) ÷ 15

Calculate the product on the right and get:

x = 54600 ÷ 15

Solved:

x = 3640

So, x equals 3640.