The value of $52-[18÷3+3+(18-11)\text{ of }4]$ is equal to:

To solve the expression, apply the BODMAS rule (Brackets, Of, Division, Multiplication, Addition, Subtraction):
First, simplify the terms inside the parentheses $()$:

$$(18-11)=7$$

The expression becomes:

$$52-[18÷3+3+7\text{ of }4]$$

Next, perform the 'of' operation:

$$7\text{ of }4=7\times 4=28$$

The expression becomes:

$$52-[18÷3+3+28]$$

Now, perform the division inside the square brackets:

$$18÷3=6$$

The expression becomes:

$$52-[6+3+28]$$

Perform the addition inside the square brackets:

$$[6+3+28]=[9+28]=37$$

Finally, perform the subtraction:

$$52-37=15$$