To solve the equation \((x+1) + (x+4) + (x+7) + \ldots + (x+28) = 155\), we first need to understand the structure of the series.

The series \((x+1), (x+4), (x+7), \ldots, (x+28)\) is an arithmetic series where each term increases by 3. Let's identify the number of terms in this series.

The first term \(a\) is \(x+1\).
The common difference \(d\) is 3.
The last term \(l\) is \(x+28\).

We can use the formula for the \(n\)-th term of an arithmetic series:
\[ a_n = a + (n-1)d \]

Setting \(a_n = x + 28\), we get:
\[ x + 28 = (x + 1) + (n-1) \cdot 3 \]

Solving for \(n\):
\[ x + 28 = x + 1 + 3(n-1) \]
\[ x + 28 = x + 1 + 3n - 3 \]
\[ 28 = 1 + 3n - 3 \]
\[ 28 = 3n - 2 \]
\[ 30 = 3n \]
\[ n = 10 \]

So, there are 10 terms in the series.

The sum \(S_n\) of the first \(n\) terms of an arithmetic series is given by:
\[ S_n = \frac{n}{2} \cdot (a + l) \]

Substituting \(n = 10\), \(a = x + 1\), and \(l = x + 28\):
\[ S_{10} = \frac{10}{2} \cdot ((x + 1) + (x + 28)) \]
\[ S_{10} = 5 \cdot (2x + 29) \]
\[ S_{10} = 10x + 145 \]

We know that the sum of the series is 155:
\[ 10x + 145 = 155 \]

Solving for \(x\):
\[ 10x = 155 - 145 \]
\[ 10x = 10 \]
\[ x = 1 \]

Thus, the value of \(x\) is \(1\).