We are asked to find the complex number \( z \) that satisfies the equation:

\[

(1+i)z - 2z^* = -11 + 25i

\]

where \( z^* \) denotes the conjugate of \( z \). Let \( z = x + yi \), where \( x \) and \( y \) are real numbers. Then, the conjugate \( z^* \) is given by:

\[

z^* = x - yi

\]

### Step 1: Substitute \( z = x + yi \) and \( z^* = x - yi \) into the equation

Substituting these into the equation, we get:

\[

(1+i)(x + yi) - 2(x - yi) = -11 + 25i

\]

### Step 2: Expand the terms

First, expand \( (1+i)(x + yi) \):

\[

(1+i)(x + yi) = 1 \cdot x + 1 \cdot yi + i \cdot x + i \cdot yi = x + yi + xi + i^2y = (x - y) + i(x + y)

\]

Next, expand \( -2(x - yi) \):

\[

-2(x - yi) = -2x + 2yi

\]

Substituting these into the equation:

\[

(x - y + 2y)i + (x - 2x - y) = -11 + 25i

\]

### Step 3: Combine like terms

Combining the real parts and imaginary parts, we have:

\[

(x - y - 2x) + (2y + x + 2yi) = -11 + 25i

\]

This simplifies to:

\[

-x - y + 2yi + (x - 2x) + (y + y)i = -11 + 25i

\]

### Step 4: Equate real and imaginary parts

Now, equate the real and imaginary parts of the equation:

For the real part:

\[

x - 2y = -11

\]

For the imaginary part:

\[

x + 2y = 25

\]

### Step 5: Solve the system of equations

We now solve the system of equations:

\[

x - 2y = -11

\]

\[

x + 2y = 25

\]

Add these two equations:

\[

(x - 2y) + (x + 2y) = -11 + 25

\]

This simplifies to:

\[

2x = 14

\]

So:

\[

x = 7

\]

Substitute \( x = 7 \) into one of the original equations:

\[

7 - 2y = -11

\]

Solve for \( y \):

\[

-2y = -18 \quad \Rightarrow \quad y = 9

\]

### Step 6: Write the complex number \( z \)

The complex number \( z \) is:

\[

z = x + yi = 7 + 9i

\]

Thus, the solution is:

\[

\boxed{7 + 9i}

\]