To solve this expression, we need to first simplify the terms inside the parentheses before multiplying the entire expression by -1 11/42.

Starting with the terms inside the parentheses:
1 16/21 ÷ 3 4/9
Convert both mixed numbers to improper fractions:
(1 21 + 16)/21 = 37/21
(3 9 + 4)/9 = 31/9

Now, divide the two fractions:
37/21 ÷ 31/9 = 37/21 x 9/31 = 333/651 = 111/217

Now, we can plug the results back into the original expression:
1 5/7 + (-6) + 111/217

Now, convert the mixed number to an improper fraction:
(1 * 7 + 5)/7 = 12/7

Add the fractions:
12/7 + (-6) + 111/217

Now find a common denominator for all the fractions and add them together:
12/7 + (-42/7) + 111/217
= (12 - 42 + 1117) / 7217
= (-30 + 777) / 1519
= 747 / 1519

Finally, multiply the result by -1 11/42:
747/1519 x -1 11/42
Convert -1 11/42 to an improper fraction:
= -1 * 42 + 11 / 42
= -53/42

Multiply the fractions:
747/1519 x -53/42 = -39369/63858

Therefore, the final result is -39369/63858.

So, the value of 1 5/7:(-6)+(1 16/21-3 4/9) ×(-1 11/42) is -39369/63858.