To solve the equation, we need to find the value of x.

First, let's simplify the expression on the left side of the equation:
4/5 + 5/7

To add fractions, we need to find a common denominator. In this case, the common denominator is 5 * 7 = 35.

So, we rewrite the fractions with the common denominator:
(4/5) * (7/7) + (5/7) * (5/5)
= 28/35 + 25/35

Now, we can add the fractions:
= (28 + 25)/35
= 53/35

Now, let's rewrite the equation with the simplified expression:
53/35 : x = 1/6

To solve for x, we can multiply both sides of the equation by the reciprocal of 53/35, which is 35/53:
(53/35 : x) * (35/53) = (1/6) * (35/53)
1 * (35/53) = (1/6) * (35/53)
35/53 = 35/318

Therefore, the value of x is 35/318.